1/9x+2=15/x-2

Solution for 1/9x+2=15/x-2 equation:

1/9x+2=15/x-2

We move all terms to the left:

1/9x+2-(15/x-2)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

1/9x-15/x+2+2=0

We calculate fractions


x/9x^2+(-135x)/9x^2+2+2=0

We add all the numbers together, and all the variables

x/9x^2+(-135x)/9x^2+4=0

We multiply all the terms by the denominator


x+(-135x)+4*9x^2=0

Wy multiply elements

36x^2+x+(-135x)=0

We get rid of parentheses

36x^2+x-135x=0

We add all the numbers together, and all the variables

36x^2-134x=0

a = 36; b = -134; c = 0;
Δ = b2-4ac
Δ = -1342-4·36·0
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-134}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+134}{2*36}=\frac{268}{72}
=3+13/18
$